black's academy
London
AQA A level Mathematics 7357 AS level Mathematics 7356 GCSE higher level
Mathematics 8300H GCSE foundation level Mathematics 8300F Edexcel A level
Mathematics 9MA0 AS level Mathematics 8MA0 GCSE higher level Mathematics 1MA1H
GCSE foundation level Mathematics 1MA1F OCR A level Mathematics H240 AS level
Mathematics H230 GCSE higher level Mathematics J560 GCSE foundation level
Mathematics Other courses IGCSE extended level Mathematics 0580 Scholastic
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symbol Director Peter Fekete Educational consultancy | Curriculum design |
Courses for adults | Public speaking | Publications CONTACT a CONTENT OF THE
REMOTE LEARNING SYSTEM * US GRADE 6 / UK GCSE GRADE 2–3 1. Addition and
subtraction 2. Starting number sequences 3. Further number sequences part I 4.
Multiplication to 8 x 8 5. Further number sequences part II 6. Multiplication to
12 x 12 7. Square numbers 8. Positive and negative numbers 9. Sums 10. Shapes
and perimiters 11. Measurement and areas 12. Reading information 14.
Understanding fractions 15. Decimals 16. Percentages 17. Long multiplication 18.
Beginning algebra 19. Beginning probability 20. Beginning geometry 21.
Properties of numbers 22. Telling the time 23. Geometry in three dimensions US
GRADE 7 / UK GCSE GRADE 4 1. Deeper understanding of number 2. Combinations 3.
Long division 4. Operations 5. Practical problems 6. Order and type of numbers
7. Measurement 8. Time and time management 9. Fractions 10. Organising
information 11. Ratio and proportion 12. Probability 13. Angles 14. Visual
reasoning 15. Bearings 16. Working in two dimensions 17. Working in three
dimensions 18. Transformation geometry 19. Continuing algebra US GRADE 8 / UK
GCSE GRADE 5–6 1. Patterns and pattern recognition 2. Lines, regions and
inequalities 3. Mastering fractions 4. Types of number 5. More about triangles
6. Measurement and computation 7. Proportionality 8. Working with space 9.
Indices 10. Further work with ratio 11. Investments 12. Further algebra 13.
Quadrilaterals and polygons 14. Speed and displacement 15. Continuing with
probability 16. Describing data US GRADE 9 / UK GCSE GRADE 6–7 1. Further
proportionality 2. Congruency 3. The tricky aspects of algebra 4. Lines and
equations 5. Basic formal algebra 6. Analysis and display of data 7. Graphing
functions 8. Dimension and algebra 9. Algebraic fractions 10. Circle theorems
11. Algebraic factors 12. Simultaneous equations 13. Velocity and acceleration
14. Proportionality and scatter 15. Number puzzles US GRADE 10/ UK GCSE GRADE
7–8 1. Transpositions 2. Patterns and pattern recognition 3. Algebraic
manipulations 4. Quadratics 5. Surds 6. Linear inequalities 7. Functions 8.
Trigonometry 9. Systems of linear equations 10. Further presentation and
analysis of data 11. Polynomial functions 12. Algebraic products 13. Finding
roots 14. Intersection of lines and curves 15. Indices and index equations US
GRADE 11/ UK GCSE GRADE 8–9 1. Completing the square 2. Venn diagrams 3.
Coordinate geometry with straight lines 4. Further trigonometry 5.
Transformations of curves 6. Modulus 7. Basic vectors 8. Quadratic inequalities
9. The quadratic discriminant 10. Arcs, sectors and segments 11. Circles, curves
and lines 12. Probability and Venn diagrams 13. Functions, domains and inverses
14. Trigonometric functions 15. Recurrence relations 16. Further elementary
vectors FREE LEGACY RESOURCES Business Studies, Economics, History, Mathematics,
Philosophy, Sociology Business Studies PEOPLE AND ORGANISATIONS 1. Management
structures and organisations 2. Leadership and management styles 3. Classical
theory of motivation 4. Human relations school 5. Management by objectives 6.
Workforce planning 7. Recruitment 8. Payment systems MARKETING 1. The economic
problem 2. Money and exchange 3. Price determination 4. Determinants of demand
5. Market analysis 6. Marketing and the product life cycle 7. Objectives and
marketing EXTERNAL INFLUENCES 1. Stakeholders 2. Business ethics 3. Market
conditions 4. Business and the trade cycle 5. Business and technological change
6. Business and inflation 7. Business and exchange rates 8. Business and
unemployment ACCOUNTING & FINANCE 1. Cash Flow Management 2. Costs, Profits &
Breakeven Analysis 3. Budgeting & Variance Analysis 4. Sources of Finance 5.
Profit & Loss Account 6. The Balance Sheet 7. Depreciation by the fixed-rate
method 8. Reducing Balance Method 9. Stock Evaluation 10. Working Capital and
Liquidity 11. Accounting Principles and Window Dressing 12. Costing and
Management Accounting 13. Investors and the Corporate Life Cycle 14. Investment
Appraisal: Average Rate of Return 15. Investment Appraisal: Payback Method 16.
Investment Appraisal: Net Present Value 17. Investment Appraisal: Internal Rate
of Return 18. Profitability Ratios 19. Liquidity Ratios 20. Efficiency and
shareholder ratios 22. Gearing and Risk 23. Net Asset Value Economics MARKETS &
MARKET FAILURE 1. The economic problem 2. Productive and allocative efficiency
3. Money and exchange 4. Price determination 5. The money market 6. Introduction
to the labour market 7. The determinants of demand 8. Supply and elasticity of
supply 9. Excess supply and excess capacity 10. Elasticity of demand 11. Market
structures 12. Income and cross elasticity 13. Market failure 14. Factor
immobility 15. Public and private goods 16. Merit and non-merit goods 17.
Cost-benefit analysis 18. Competition policy 19. Market failure and government
intervention History ANCIENT HISTORY 1. Prehistory of Greece 2. Mycenae, the
Heroic Age c.1550—1125 BC 3. The Greek Middle Ages c.1125—c.700 BC 4. The Greek
Tyrannies c. 650—510 BC 5. Sparta 6th and 7th centuries BC 6. Athens and Solon
7. The early inhabitants of Italy 8. The Etruscans 9. Early Roman History up to
Tarquin GERMANY & EUROPE 1870—1939 1. Social Change from 1870 to 1914 2.
Socialism in Europe 1870 to 1914 3. The Balance of Power in Europe 1870 4. Anti
Semitism in Europe 1870 to 1914 5. The Structure of Wilhelmine Germany 6.
Bismarck and the Alliance System 7. Weltpolitik 8. Colonial Rivalries 9. First
and Second Moroccan Crises 10. The First World War triggers 11. The Causes of
the First World War 12. Germany and the First World War 13. Military history of
the First World War 14. The Treaty of Versailles 15. The Domestic Impact of the
First World War 16. The German Revolution 17. The Weimar Republic 18. The Early
Years of the Nazi Party 19. The Rise of the Nazi Party 20. The Establishment of
the Nazi Dictatorship 21. Nazi Rule in Germany 1934 to 1939 22. The Economics of
the Third Reich 23. Appeasement RUSSIA & EUROPE 1855—1953 1. Alexander II and
the Great Reforms 2. Imperial Russia under Alexander III 3. Nicholas II and the
1905 revolution 4. Social and economic developments in Russia 5. Russia: the
Great war and collapse of Tsarism 6. Provisonal Government & October Revolution
7. The Era of Lenin 8. The Development of Lenin's Thought 9. New Economic Policy
and the Rise of Stalin 10. Stalin and the Soviet Union 1924 to 1953 11. Stalin
and the Soviet Economy 12. Stalin and International Relations BRITAIN 1914—1936
1. The Great War and Britain 1914—15 2. Britain during the Great War, 1915—16 3.
Lloyd George & the Great War, 1916—1918 4. Great Britain after the War, 1918—22
5. British Politics, 1922—25 6. Class Conflict & the National Strike, 1926 7.
Britain & International Relations, 1925—29 8. Social Trends in Britain during
the 1920s 9. Social Issues during the late 1920s 10. British Politics 1926—29;
Election of 1929 11. Britain — the crisis of 1929 12. The Labour Government of
1929—31 13. Britain and economic affairs, 1931—33 14. Britain and Foreign
Affairs, 1931—36 15. Social Conditions in Britain during the 1930s Advanced
level Mathematics ALGEBRA & GEOMETRY 1. Simultaneous Equations 2. Polynomial
Algebra 3. Cartesian Coordinates 4. The equation of the straight line 5.
Intersection of lines and curves 6. Remainder and Factor Theorems 7. Functions
8. Quadratic Inequalities 9. Graphs of Inequalities 10. Indices 11. Polynomial
Division 12. Velocity-Time Graphs 13. Tally Charts 14. Absolute and relative
errors 15. Sequences and Series 16. Arithmetic Progressions 17. Proof by
Contradiction 18. Geometric Progressions 19. The Cartesian Equation of the
Circle 20. Transformations of graphs 21. Plane Trigonometry 22. Modulus 23.
Trigonometric Functions 24. Inverse Trigonometric Functions 25. Linear
Inequalities 26. Proportionality 27. Probability 28. Surds 29. Special Triangles
30. Quadratic Polynomials 31. Roots & Coefficients of Quadratics 32. Radian
measure 33. Permutations and Combinations 34. Set Theory and Venn Diagrams 35.
Sine and cosine rules 36. Elementary Trigonometric Identities 37. Roots and
curve sketching 38. Graphs and roots of equations 39. Picards Method 40. Small
Angle Approximations 41. Simultaneous equations in three unknowns 42. Linear
relations and experimental laws 43. Conditional Probability 44. Pascal's
Triangle and the Binomial Theorem 45. Index Equations and Logarithms 46. The
Binomial Theorem for Rational Indices 47. Exponential Growth and Decay 48.
Exponential and Natural Logarithm 49. Compound Angle Formulas 50. Sinusoidal
functions 51. Vector Algebra 52. The Vector Equation of the Straight Line 53.
The Scalar Product of Vectors 54. Axiom Systems 55. Introduction to Complex
Numbers 56. The algebra of complex numbers 57. Complex Numbers and the Argand
plane 58. De Moivres Theorem 59. Eulers formula 60. Further loci of complex
numbers 61. Further graph sketching 62. Mathematical Induction 63. Proof of the
Binomial Theorem 64. Polar Coordinates 65. Conic sections 66. Partial Fractions
67. First-order linear recurrence relations 68. Summation finite series with
standard results 69. Method of differences 70. Trigonometric Equations 72.
Series Expansion 73. Lagrange Interpolating Polynomial 74. Error in an
interpolating polynomial 75. Abelian groups 76. Geometrical uses of complex
numbers 77. Cyclic Groups 78. The Cayley-Hamilton Theorem 2x2 Matrices 79.
Cayley Theorem 80. Determinants 81. Isomorphisms 82. Lagrange theorem 83.
Properties of groups 84. Group structure 85. Subgroups 86. Homomorphisms 87.
Matrix Algebra 88. Determinant and Inverse of a 2x2 matrix 89. Gaussian
elimination 90. Matrix representation of Fibonacci numbers 91. Matrix groups 92.
Inverse of a 3 x 3 Matrix 93. Singular and non-singular matrices 94. Properties
of Matrix Multiplication 95. Induction in Matrix Algebra 96. Properties of
Determinants 97. Permutation groups 98. First Isomorphism Theorem for Groups 99.
Roots of Polynomials of Degree 3 100. Scalar Triple Product 101. Systems of
Linear Equations 102. Matrix Transformations 103. Mappings of complex numbers
104. Cross product of two vectors 105. Vector planes 106. Eigenvalues and
Eigenvectors CALCULUS 1. Introduction to the Differential Calculus 2. Stationary
points and curve sketching 3. Applications of Differentiation 4. Differentiation
from First Principles 5. The Trapezium Method 6. Integration 7. Direct
Integration 8. Applications of integration to find areas 9. Graphs of Rational
Functions 10. Derivatives of sine and cosine 11. Products, Chains and Quotients
12. Volumes of Revolution 13. Exponential and Logarithmic Functions 14.
Integration by Parts 15. Parametric Equations 16. The Integral of 1/x 17.
Integration by Substitution 18. Implicit Differentiation 19. Formation of a
differential equation 20. Separation of variables 21. Integrals of squares of
trig functions 22. Maclaurin Series 23. Techniques of Integration 24.
Integrating Factor 25. The Newton-Raphson formula 26. Errors in Numerical
Processes 27. Roots and Recurrence Relations 28. Derivatives of Inverse Trig.
Functions 29. Second order homogeneous equations 30. Second order inhomogeneous
equations 31. Implicit differentiation — second derivative 32. Integrands to
inverse trigonometric functions 33. Integrands to logarithmic function 34.
Integration of Partial Fractions 35. Logarithms and Implicit Differentiation 36.
Implicit differentiation and MaClaurin series 37. Separation of variables by
substitution 38. Trigonometric Substitutions for Integrals 39. Truncation Errors
40. Euler and Trapezoidal Method 41. Numerical methods for differential
equations 42. Simpson Method 43. Proof of Simpson Formula 44. Richardson
Extrapolation 45. Arc length of a curve in Cartesian coordinates 46. Arc length
of a curve in Polar coordinates 47. Arc length of a curve: Parametric form 48.
Curves in Euclidean space 49. Functions and continuity 50. The gradient of a
scalar field 51. The derivatives of the hyperbolic functions 52. Hyperbolic
Functions 53. Inverse Hyperbolic Functions 54. Hyperbolic Identities 55.
Integrals with inverse hyperbolic functions 56. Reduction formulae 57.
Simultaneous differential equations 58. Surface of Revolution 59. Vector
differential calculus 60. Scalar Fields and Vector Functions STATISTICS &
PROBABILITY 1. Central Tendency: Mean, Median and Mode 2. Standard Deviation 3.
Cumulative Frequency 4. Discrete Random Variables 5. Mutually exclusive and
independent events 6. The Binomial Distribution 7. The Normal Distribution 8.
Standardised Normal Distribution 9. Regression Lines 10. Correlation 11. The
Geometric Distribution 12. Hypothesis Testing — Binomial Distribution 13. Index
Numbers 14. Time Series Analysis 15. Bayes Theorem 16. Confidence interval mean
— known variance 17. The Central Limit Theorem 18. Pearsons product moment
correlation 19. Spearmans Rank Correlation Coefficient 20. Hypothesis Testing —
Normal Distribution 21. The Poisson Distribution 22. The Normal Approximation to
the Binomial 23. The Normal Approximation to the Poisson 24. The Poisson
Approximation to the Binomial 25. Type I and type II errors 26. Scalar multiples
of a Poisson variable 27. Test for the Mean of a Poisson distribution 28. Random
Number Sampling 29. Estimating Population Parameters 30. Random Samples and
Sampling Techniques 31. The Concept of a Statistic 32. Hypothesis test for the
population variance 33. Central Concepts in Statistics 34. Continuous
Probability Distributions 35. Modeling: Chi squared goodness of fit 36. Chi
squared test for independence 37. Degrees of Freedom 38. Difference Sample Means
Unknown Variance 39. Moment generating functions 40. Probability generating
functions 41. Linear Combinations of Random Variables 42. Maximum Likelihood
Estimators 43. Wilcoxon signed rank test on median 44. Non-parametric
significance tests 45. Single-sample sign test of population median 46.
Paired-sample sign test on medians 47. Paired sample t-test for related data 48.
Paired sample Wilcoxon signed rank test 49. Difference of two sample means 50.
Pooled sample estimate 51. Testing the Sample Mean 52. The Uniform Distribution
MECHANICS 1. Velocity-Time and Displacement-Time Graphs 2. Force diagrams 3.
Representation of Forces by Vectors 4. Static Equilibrium 5. Equilibrium of
coplanar forces 6. Weight and Free Fall 7. Normal Reaction and Friction 8.
Newtons First and Second Laws 9. Relative Motion 10. Projectiles 11. Calculus
and Kinematics 12. Motion of a Particle: Vector calculus form 13. Work 14.
Energy Conversions 15. Gravitational potential and kinetic energy 16. Connected
Particles 17. Moments 18. Linear momentum 19. Power 20. Hookes Law 21. Simple
Harmonic Motion 22. Simple Harmonic Motion and Springs 23. Calculus, Kinematics
in Three Dimensions 24. Sliding, toppling and suspending 25. Impulsive Tensions
in Strings 26. Angular Velocity 27. Motion in a Horizontal Circle 28. Centre of
Mass of a Uniform Lamina 29. Motion in a Vertical Circle 30. Motion under a
Variable Force 31. Conservation of Angular Momentum 32. Centre of Mass of a
Composite Body 33. Motion under a central force 34. Centre of Mass of a Uniform
Lamina 35. Centre of Mass Uniform Solid of Revolution 36. Equilibrium of Rigid
Bodies in Contact 37. Damped Harmonic Motion 38. Moment of Inertia 39. Impulse,
elastic collisions in one dimension 40. Parallel and Perpendicular Axis Theorems
41. Motion described in polar coordinates 42. Simple pendulum 43. Compound
pendulum 44. Stability and Oscillations 45. Vector calculus 46. Linear Motion of
a Body of Variable Mass DISCRETE & DECISION 1. Algorithms 2. Introduction to
graph theory 3. Dijkstra algorithm 4. Sorting Algorithms 5. Critical Path
Analysis 6. Dynamic Programming 7. Decision Trees 8. The Maximal Flow Problem 9.
The Hungarian algorithm 10. Introduction to Linear Programming 11. Simplex
Method 12. Matching Problems 13. Game Theory 14. Minimum connector problem 15.
Recurrence relations 16. Proofs for linear recurrence relations 17. Simulation
by Monte Carlo Methods 18. Travelling and Optimal Salesperson Problems 19. The
Travelling Salesperson Problem Philosophy INTRODUCTION TO PHILOSOPHY 1. The
problem of evil 2. Introduction to Plato 3. Knowledge, belief and justification
4. Descartes Meditation I 5. Introduction to the problem of universals 6.
Introduction to metaethics 7. Subjectivism versus objectivism 8. Aristotle's
function argument 9. Natural Law Theory 10. Utilitarianism 11. The Nicomachaen
Ethics of Aristotle 12. Virtue Ethics 13. Descartes Meditation II 14. Hume and
empiricism 15. The paradox of induction 16. Hume's attack on Descartes 17. The
Cosmological Argument 18. The Ontological Argument 19. The Teleological Argument
20. The Argument from religious experience 21. The Moral Argument 22. The
argument from illusion 23. Materialism 24. Human Identity Sociology PERSPECTIVES
& METHODOLOGY 1. Introduction to Marxism 2. Introduction to Durkheim 3. Weber:
classes, status groups and parties 4. Introduction to patriarchy and gender
roles 5. Mass culture theory 6. The Frankfurt school STRATIFICATION & DIVERSITY
1. Ethnic groups and discrimination 2. Race, Ethnicity and Nationalism 3. Social
Inequality 4. Theories of Racism 5. Class structure 6. Modern Functionalism and
Stratification 7. Social Mobility 8. Bottomore: Classes in Modern Britain 9.
American exceptionalism ASPECTS OF SOCIETY 1. Definitions of Poverty 2. Theories
of Poverty 3. Solutions to Poverty 4. Alienation 5. Leisure 6. Work and
Technological Change 7. Conflict and Cooperation at Work 8. Attitudes to Work 9.
Unemployment 10. Perspectives on Education 11. Education and Ethnicity 12.
Education and Gender 13. The Family and Social Structure 14. The Family and
Household Structure 15. Conjugal Roles 16. Marital Breakdown 17. Post War
Education in Britain 18. British Social Policy 1945—1990
